Theoretical physicists think that magnetic monopoles must exist. In 1931 Dirac showed that the existence of magnetic monopoles could explain the quantization of electric charge. The existence of magnetic monopole also makes the Maxwell equations with sources symmetric with respect to electric and magnetic fields. Also, some grand unified theories (t’Hooft 1974, Polyakov 1974) predict the existence of small numbers of these particles .
The term “magnetic monopole” refers to an elementary particle or a formation such as a soliton. There is no experimental evidence for elementary magnetic monopoles yet.
There are composite formations that can be described as “artificial magnetic monopoles.” These have been created in the laboratory. These artificial magnetic monopoles are magnetic whirls. They are also known as skyrmions.
The experimental searches for elementary magnetic monopoles are listed at the PDG site.